Chapter 5 Review

5.1 covers fundamental indentities. These are used in trigonometry to evaluate functions, simplify expressions, and solve equations. You do not need to memorize these for the final (or any other formulas from this chapter), but some examples are:

Reciprocal
csc(x)=1/sin(x)

Quotient
tan(x)=sin(x)/cos(x)

Pythagorean
sin^2(x)+cos^2(x)=1

Cofunction
sin((pi/2)-x)=cos(x)

Even/Odd
cot(-x)=-cot(x)


5.2 goes over verifying identities. Some guidelines are:

1. Work with one side of the equation at a time, preferably the more complicated side.
2. Look for opportunities to factor an expression, add fractions, square a binomial, or create a common denominator.
3. Look for opportunities to use the fundamental identities. Note which functions are in the final expression you want.
4. Try converting terms to sines and cosines.

For help with sections 5.1 and 5.2: http://www.youtube.com/watch?v=pviWtesNnAY&feature=related

5.3 covers solving trigonometric equations. When solving an equation try:

1. Combining like terms
2. Taking squares and square roots
3. Factoring
4. Rewriting trigonometric functions
5. Using inverse functions

5.4 goes over the sum and difference formulas. These are used in identities and to evaluate values that aren't on the unit circle. Here are some examples:

cos(x+y)=cos(x)cos(y)-sin(x)sin(y)

sin(x+y)=sin(x)cos(y)+cos(x)sin(y)

5.5 covers multiple-angle and product-sum formulas. An example of a double-angle formula is:

• sin(2x)=2sin(x)cos(x)

An example of a power-reducing formula is:

• cos^2(x)=(1+cos(2x))/2

An example of a half-angle formula is:

• tan(x/2)=(1-cos(x))/sin(x)=sin(x)/(1+cos(x))

An example of a product-to-sum formula is:

• sin(x)cos(y)=1/2(sin(x+y)+sin(x-y))

And an example of a sum-to-product formula is:

• cos(x)+cos(y)=2cos((x+y)/2)cos((x-y)/2)

Good luck everyone!